Seminar on Reckoning

Ideals on natural numbers and combinatorial characterization of sigma-ideal N

Viera Šottová

IM CAS

Seminar on Reckoning

Wednesday, 17. July 2019 - 11:00 to 15:00

Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building

Historically, there is a lot of interesting results about Cichoń's diagram as well as corresponded objects. Particularly, Bartoszyński adduced several nice combinatorial characterizations of notions which we are interested in.

We mainly study an ideal of Lebesgue measure zero sets, denoted N and we briefly modify its characterization with respect to ideals on natural numbers. We obtain a family N_J which is sigma-ideal as well. Additionally, it is a subset of N. On the other hand, N_J expresses a connection between ideals on natural numbers and ideals on real line. We deal with common cardinal invariants of such families and their relation to original notion.

Joint work with D. A. Mejia

We mainly study an ideal of Lebesgue measure zero sets, denoted N and we briefly modify its characterization with respect to ideals on natural numbers. We obtain a family N_J which is sigma-ideal as well. Additionally, it is a subset of N. On the other hand, N_J expresses a connection between ideals on natural numbers and ideals on real line. We deal with common cardinal invariants of such families and their relation to original notion.

Joint work with D. A. Mejia